Evidence of Supercritical Behavior in Liquid Single Crystal Elastomers A. Lebar, 1 Z. Kutnjak, 1 S. Z ˇ umer, 2,1 H. Finkelmann, 3 A. Sa ´nchez-Ferrer, 3 and B. Zalar 1 1 J. Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia 2 Department of Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia 3 Institut fu ¨r Makromolekulare Chemie, Universita ¨t Freiburg, D-79104 Freiburg, Germany (Received 30 November 2004; published 16 May 2005) Temperature profiles of the first and the second moment of the nematic order parameter distribution function, as determined from the deuteron nuclear magnetic resonance line shapes, as well as heat capacity response, provide support for the supercritical scenario of the nematic-paranematic phase transition in liquid single crystal elastomers. The relative strength of the locked-in internal mechanical field with respect to the critical field can be decreased by swelling the elastomer samples with low molecular mass nematogen. By increasing the concentration of the dopant, critical and below-critical behavior is promoted. DOI: 10.1103/PhysRevLett.94.197801 PACS numbers: 64.70.Md, 76.60.2k, 82.70.2y One of the major open problems in the physics of liquid single crystal elastomers (LSCE) is the nature of the isotropic-nematic phase transition, particularly in view of the question of whether the elasticity in these materials is of the soft, semisoft, or non-soft-type [1]. It was demon- strated [2,3] that the shape of the stress-strain diagram is strongly related to the orientational order of the nematic director field. The degree of this order crucially depends on the crosslinking history of the sample [4]. The debate about the applicability of the concept of soft elasticity to LSCEs has been recently reopened by the measurements of dy- namical shear modulus [5]. Conventional nematogenic liquid crystals exhibit a first-order phase transition, easily identifiable by a discontinuous jump of the nematic order parameter (OP) ST at the clearing temperature T NI , ob- served in birefringence measurements [6] or deuteron nu- clear magnetic resonance (DNMR) [7] and by a dis- continuous jump of the enthalpy observed in calorimetric experiments [8]. In LSCEs, on the contrary, the onset of the nematic order is continuous [7], with a transition from the paranematic (PN) phase with small S to the nematic (N) phase with large S that takes place within a relatively narrow temperature interval (typically a few K). In view of the application potential of these materials for actuator and biomimetic devices (like artificial muscles) [9], the understanding of the physical mechanisms leading to the smearing out of the ST profile could contribute to the optimization of the temperature response of mechanical strain, eT/ ST, for various applications. There exist two radically different descriptions of the N-PN phase transition in LSCEs. The first one considers them as inherently heterogeneous materials [10], com- posed of domains, each with a well-defined set of Landau –de Gennes (LdG) free energy expansion coeffi- cients. The average OP temperature profile of the system, S av T, is then calculated as a superposition of profiles ST arising from the individual microdomains. Alterna- tively, the behavior of ST  in LSCEs can be attributed to the supercritical character of the N-PN transition [11]. It is a well-known fact that a linear coupling of the nematic OP with a conjugate internal or external field g, accounted for by the free energy term gS, can drive the transition to a supercritical regime, characterized by zero latent heat and continuous ST profile. This occurs whenever g exceeds the critical value g c . In LSCEs, g is the mechanical stress field that consists of the internal, monodomain-state main- taining field g int , imprinted into the system during the two- step ‘‘Finkelmann crosslinking procedure’’ [12] and the external field g ext , applied by straining the sample. The ‘‘heterogeneous’’ and ‘‘supercritical’’scenaria, de- scribed above, both provide for qualitatively satisfactory description of the OP temperature profile in LSCEs. In order to distinguish between the two scenaria, Selinger et al. exploited the fact that, in the N-PN transition region, the two models predict slightly mismatching ST curves [10]. They found the internal field to be far below the critical value g int =g c  0:2–0:5, a result quite unexpected. In this Letter, we present a novel experimental method which allows for a clear-cut discrimination between the two proposed N-PN transition scenaria. We show that LSCEs, prepared by the ‘‘Finkelmann procedure,’’ are supercritical systems with relatively low heterogeneity. We also demonstrate that, when doped with an increasing amount of conventional nematogen, they can be driven towards the critical regime. The method is based on the analysis of the temperature profiles of the first and second moments of DNMR spectra of deuterated mesogenic mole- cules. Our approach has two advantages over the previous study [10]. First, the primary OP ST is analyzed rather than the secondary OP eT, and, second, we overcome the problems with low resolution, arising from the fact that the experimental error of the eT points is of the same order of magnitude as the difference between the theoretical eT points of the heterogeneous and supercritical scenaria. The results of the DNMR method are supported by the ac and relaxation calorimetric data. Side-chain LSCE materials based on poly- [oxy(methylsilylene)] were synthesized as described in PRL 94, 197801 (2005) PHYSICAL REVIEW LETTERS week ending 20 MAY 2005 0031-9007= 05=94(19)=197801(4)$23.00 197801-1  2005 The American Physical Society